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Restricted Edge-colourings of Bipartite Graphs

Published online by Cambridge University Press:  12 September 2008

Roland Häggkvist
Roland Häggkvist
Affiliation:
Department of Mathematics, University of Umeå, S-90187, Umeå, Sweden
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Abstract

Suppose each vertex of a bipartite multigraph (with partition (X, Y)) is assigned a set of colours; we say this colour scheme is feasible if the edges of the graph can be properly coloured so that each receives a colour in both of its endpoints' sets. We prove various results showing that certain types of colour scheme are always feasible. For instance, we prove that if the colour scheme obtained by assigning the set {1,…, d(x)} of colours to each vertex x of X and the set T = {1,…, t} (t < Δ(X)) to each vertex of Y is feasible, then so is every colour scheme where each vertex x of X gets d(x) colours from T and each vertex of Y gets the set T.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 385 - 392
Copyright
Copyright © Cambridge University Press 1996

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References

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